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Journal articles on the topic 'Differential filtration'

Author: Grafiati

Published: 30 May 2022

Last updated: 19 July 2025

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1

Abrashkin, Viktor Aleksandrovich. "Ramification filtration and differential forms." Izvestiya: Mathematics 87, no. 3 (2023): 421–38. http://dx.doi.org/10.4213/im9322e.

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Let $L$ be a complete discrete valuation field of prime characteristic $p$ with finite residue field. Denote by $\Gamma_{L}^{(v)}$ the ramification subgroups of $\Gamma_{L}=\operatorname{Gal}(L^{\mathrm{sep}}/L)$. We consider the category $\operatorname{M\Gamma}_{L}^{\mathrm{Lie}}$ of finite $\mathbb{Z}_p[\Gamma_{L}]$-modules $H$, satisfying some additional (Lie)-condition on the image of $\Gamma_L$ in $\operatorname{Aut}_{\mathbb{Z}_p}H$. In the paper it is proved that all information about the images of the groups $\Gamma_L^{(v)}$ in $\operatorname{Aut}_{\mathbb{Z}_p}H$ can be explicitly extracted from some differential forms $\widetilde{\Omega} [N]$ on the Fontaine etale $\phi $-module $M(H)$ associated with $H$. The forms $\widetilde{\Omega}[N]$ are completely determined by a canonical connection $\nabla $ on $M(H)$. In the case of fields $L$ of mixed characteristic, which contain a primitive $p$th root of unity, we show that a similar problem for $\mathbb{F}_p[\Gamma_L]$-modules also admits a solution. In this case we use the field-of-norms functor to construct the corresponding $\phi $-module together with the action of the Galois group of a cyclic extension $L_1$ of $L$ of degree $p$. Then our solution involves the characteristic $p$ part (provided by the field-of-norms functor) and the condition for a "good" lift of a generator of $\operatorname{Gal}(L_1/L)$. Apart from the above differential forms the statement of this condition uses the power series coming from the $p$-adic period of the formal group $\mathbb{G}_m$.

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2

Abrashkin, Viktor Aleksandrovich. "Ramification filtration and differential forms." Известия Российской академии наук. Серия математическая 87, no. 3 (2023): 5–22. http://dx.doi.org/10.4213/im9322.

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Let $L$ be a complete discrete valuation field of prime characteristic $p$ with finite residue field. Denote by $\Gamma_{L}^{(v)}$ the ramification subgroups of $\Gamma_{L}=\operatorname{Gal}(L^{\mathrm{sep}}/L)$. We consider the category $\operatorname{M\Gamma}_{L}^{\mathrm{Lie}}$ of finite $\mathbb{Z}_p[\Gamma_{L}]$-modules $H$, satisfying some additional (Lie)-condition on the image of $\Gamma_L$ in $\operatorname{Aut}_{\mathbb{Z}_p}H$. In the paper it is proved that all information about the images of the groups $\Gamma_L^{(v)}$ in $\operatorname{Aut}_{\mathbb{Z}_p}H$ can be explicitly extracted from some differential forms $\widetilde{\Omega} [N]$ on the Fontaine etale $\phi $-module $M(H)$ associated with $H$. The forms $\widetilde{\Omega}[N]$ are completely determined by a canonical connection $\nabla $ on $M(H)$. In the case of fields $L$ of mixed characteristic, which contain a primitive $p$th root of unity, we show that a similar problem for $\mathbb{F}_p[\Gamma_L]$-modules also admits a solution. In this case we use the field-of-norms functor to construct the corresponding $\phi $-module together with the action of the Galois group of a cyclic extension $L_1$ of $L$ of degree $p$. Then our solution involves the characteristic $p$ part (provided by the field-of-norms functor) and the condition for a "good" lift of a generator of $\operatorname{Gal}(L_1/L)$. Apart from the above differential forms the statement of this condition uses the power series coming from the $p$-adic period of the formal group $\mathbb{G}_m$. Bibliography: 21 titles.

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3

Geiss, Hans C., Parhofer, Donner, and Schwandt. "Low Density Lipoprotein Apheresis by Membrane Differential Filtration (Cascade Filtration)." Therapeutic Apheresis 3, no. 3 (1999): 199–202. http://dx.doi.org/10.1046/j.1526-0968.1999.00157.x.

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4

von Baeyer, Hans, Frank Kochinke, Ingo Schwaner, Rainer Schwerdtfeger, and Wolfgang Schwarztkopff. "Fundamentals and application of differential filtration." Plasma Therapy and Transfusion Technology 8, no. 4 (1987): 273–82. http://dx.doi.org/10.1016/s0278-6222(87)80031-1.

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5

Nagase, Youichi, and Kenji Okada. "Experimental Verification of Governing Differential Equation for Filtration-Constant Pressure Cake Filtration-." Journal of the Society of Powder Technology, Japan 40, no. 11 (2003): 786–94. http://dx.doi.org/10.4164/sptj.40.786.

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6

Khodagholi, Mohammad, Mohammad Hemmati, and Ali Pour. "Efficient filtration system for paraffin-catalyst slurry separation." Chemical Industry and Chemical Engineering Quarterly 19, no. 2 (2013): 295–301. http://dx.doi.org/10.2298/ciceq120226063k.

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The filtration efficiency for separating liquid paraffin (or water) from a slurry consisting of 25 weight% spherical alumina in a Slurry Bubble Column Reactor (SBCR) comprised of a cylindrical tube of 10 cm diameter and 150 cm length was studied. Various differential pressures (?P) were applied to two separate tubular sintered metal stainless steel filter elements with nominal pore size of 4 and 16?m. The experimental results disclosed that the rate of filtrations increased on applying higher differential pressure to the filter element. Albeit this phenomenon is limited to moderate ?Ps and for ?P more than 1 bar is neither harmful nor helpful. The highest filtration rates at ?Ps higher than 1 bar were 170 and 248 ml/minute for 4 and 16?m respectively. Using water as the liquid in slurry the rate of filtration enhanced to 4 folds, and this issue reveals impact of viscosity on filtration efficiency clearly. In all situations, the total amount of particles present in the filtrate part never exceeded a few parts per million (ppm). The statistical analysis of the SEM image of the filtrate indicated that by applying higher pressure difference to the filter element the frequency percent of larger particle size increases. The operation of filter cake removing was performed with back flashing of 300 ml of clean liquid with pressures of 3-5 bar of N2 gas.

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7

Nazir, Maryam, Syed Zakir Hussain Bukhari, Jong-Suk Ro, Fairouz Tchier, and Sarfraz Nawaz Malik. "On Inequalities and Filtration Associated with the Nonlinear Fractional Operator." Fractal and Fractional 7, no. 10 (2023): 726. http://dx.doi.org/10.3390/fractalfract7100726.

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In this paper, we study a new filtration class MFα,βμ, associated with the filtration of infinitesimal generators, by using the nonlinear fractional differential operator and study certain properties, like sharp Fekete–Szegö inequalities and filtration problems.

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8

Atamanyuk, Volodymyr, and Yaroslav Gumnytskyi. "Mass Exchange Dynamics During the Second Filtration Drying Period." Chemistry & Chemical Technology 3, no. 2 (2009): 129–37. http://dx.doi.org/10.23939/chcht03.02.129.

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The work is dedicated to theoretical and experimental investigations of kinetics and dynamics of filtration drying of capillary and pore materials, and mineral granulated fertilizers, in particular. The proposed physical model of a moist particle and the differential system of equations which describes heat exchange in the second drying period enables to determine the transfer velocity of mass-exchange zone in a dispersion layer of the material during filtration drying.

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9

Ohkubo, Shun. "Logarithmic growth filtrations for -modules over the bounded Robba ring." Compositio Mathematica 157, no. 6 (2021): 1265–301. http://dx.doi.org/10.1112/s0010437x21007107.

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In the 1970s, Dwork defined the logarithmic growth (log-growth for short) filtrations for $p$-adic differential equations $Dx=0$ on the $p$-adic open unit disc $|t|<1$, which measure the asymptotic behavior of solutions $x$ as $|t|\to 1^{-}$. Then, Dwork calculated the log-growth filtration for $p$-adic Gaussian hypergeometric differential equation. In the late 2000s, Chiarellotto and Tsuzuki proposed a fundamental conjecture on the log-growth filtrations for $(\varphi ,\nabla )$-modules over $K[\![t]\!]_0$, which can be regarded as a generalization of Dwork's calculation. In this paper, we prove a generalization of the conjecture to $(\varphi ,\nabla )$-modules over the bounded Robba ring. As an application, we prove a generalization of Dwork's conjecture proposed by Chiarellotto and Tsuzuki on the specialization property for log-growth Newton polygons.

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10

Svalov, A. M. "Bottom-hole filtration at a positive differential pressure." Soviet Mining Science 25, no. 1 (1989): 56–60. http://dx.doi.org/10.1007/bf02528431.

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11

Biswas, Indranil. "Differential operators and flat connections on a Riemann surface." International Journal of Mathematics and Mathematical Sciences 2003, no. 64 (2003): 4041–56. http://dx.doi.org/10.1155/s0161171203212187.

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We consider filtered holomorphic vector bundles on a compact Riemann surfaceXequipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. IfQis a stable vector bundle of rankrand degree(1−genus(X))nr, then any holomorphic connection on the jet bundleJn(Q)satisfies this transversality condition for the natural filtration ofJn(Q)defined by projections to lower-order jets. The vector bundleJn(Q)admits holomorphic connection. The main result is the construction of a bijective correspondence between the space of all equivalence classes of holomorphic vector bundles onXwith a filtration of lengthntogether with a holomorphic connection satisfying the transversality condition and the space of all isomorphism classes of holomorphic differential operators of ordernwhose symbol is the identity map.

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12

Merkle, Ana. "Predictability and uniqueness of weak solutions of the stochastic differential equations." Analele Universitatii "Ovidius" Constanta - Seria Matematica 31, no. 1 (2023): 207–19. https://doi.org/10.2478/auom-2023-0011.

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Abstract Causality is a topic which receives much attention nowadays and it represents a prediction property in the context of possible reduction of available information in order to predict a given filtration. In this paper we define the concept of dependence between stochastic processes and between filtrations, named causal predictability, which is based on the Granger’s definition of causality. This definition extends the ones already given in the continuous time. Then, we provide some properties of the given concept. Finally, we apply the concept of causal predictability to the processes of the diffusion type, more precisely, to the uniqueness of weak solutions of the stochastic differential equations.

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13

Lužaić, Tanja, Katarina Nedić Grujin, Lato Pezo, Branislava Nikolovski, Zoran Maksimović, and Ranko Romanić. "Implementation of Cellulose-Based Filtration Aids in Industrial Sunflower Oil Dewaxing (Winterization): Process Monitoring, Prediction, and Optimization." Foods 13, no. 18 (2024): 2960. http://dx.doi.org/10.3390/foods13182960.

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In the production of refined sunflower oil, waxes are removed during the winterization stage, and wax crystals are separated through filtration assisted by filtration aids. Commonly used filtration aids in oil refining include perlite and diatomaceous earth. After winterization, a significant amount of filter cake remains as a by-product and is treated as waste. Today, natural cellulose fibers are being promoted as filtration aids. Their advantages are numerous, both in the production process and from an environmental perspective. However, their only disadvantage is their higher cost. Therefore, in this study, 57 filtration cycles during the industrial sunflower oil winterization step using cellulose-based filtration aids were monitored. Different process parameters, including the pressure differential on the filter, the flow rate of filtered oil, constant pressure period, the quantity of filtered oil, filtration time, the quantity of pre-coating and dosing filtration aids, the volume of filtered oil, the concentration of dosing filtration aid, as well as the mass of separated waxes, were observed. Additionally, artificial neural networks were applied to predict process parameters, optimize the process, and, above all, determine the dosage of filtration aids, which will make the process more economical. The optimal filtration process is performed at a pressure differential of 3.3 bar, lasting a total of 39 h, with 32 h at constant pressure, resulting in 322,503 kg of filtered oil and 90.41 kg of waxes. The optimal quantity of cellulose-based filtration aids employed for pre-coat was 80 kg, and for dosing, 375 kg, with an optimal concentration of 0.12% w/w.

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14

Alimbekova, Nurlana, Abdumauvlen Berdyshev, Muratkan Madiyarov, and Yerlan Yergaliyev. "Finite Element Method for a Fractional-Order Filtration Equation with a Transient Filtration Law." Mathematics 12, no. 16 (2024): 2519. http://dx.doi.org/10.3390/math12162519.

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In this article, a numerical method is proposed and investigated for an initial boundary value problem governed by a fractional differential generalization of the nonlinear transient filtration law which describes fluid motion in a porous medium. This type of equation is widely used to describe complex filtration processes such as fluid movement in horizontal wells in fractured geological formations. To construct the numerical method, a high-order approximation formula for the fractional derivative in the sense of Caputo is applied, and a combination of the finite difference method with the finite element method is used. The article proves the uniqueness and continuous dependence of the solution on the input data in differential form, as well as the stability and convergence of the proposed numerical scheme. The linearization of nonlinear terms is carried out by the Newton method, which allows for achieving high accuracy in solving complex problems. The research results are confirmed by a series of numerical tests that demonstrate the applicability of the developed method in real engineering problems. The practical significance of the presented approach lies in its ability to accurately and effectively model filtration processes in shale formations, which allows engineers and geologists to make more informed decisions when designing and operating oil fields.

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15

Bierck, B. R., and R. I. Dick. "In Situ Examination of Effects of Pressure Differential on Compressible Cake Filtration." Water Science and Technology 22, no. 12 (1990): 125–34. http://dx.doi.org/10.2166/wst.1990.0107.

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A synchrotron X-ray absorbance technique was used to monitor suspended solids concentration changes in compressible filter cakes formed at different constant pressure differentials. Results for a kaolin slurry and an activated sludge manifested the markedly higher compressibility of the latter sludge. A model developed to describe effects of pressure differential on filtrate production behavior of an ideal compressible slurry indicated that the kaolin slurry behaved as such. However, the activated sludge was not ideal because changes in pressure differential did not cause the idealized change in filtrate production rate. A thin skin of activated sludge solids at the filter medium accounted for the non-ideal compressive behavior. Porewater pressure data acquired 0.86 mm above the filter medium during activated sludge filtration provided evidence of skin formation and its effect - virtually the total pressure drop occurred within this 0.86 mm region throughout cake formation (after which shrinkage began). Hence, significant effective stresses required to consolidate the sludge cake did not develop in most of the cake until cake formation was complete and shrinkage began.

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16

Manolakos, Spiros, Francy Sinatra, Leila Albers, et al. "Differential Mobility Spectrometry for Inorganic Filtration in Nuclear Forensics." Analytical Chemistry 88, no. 23 (2016): 11399–405. http://dx.doi.org/10.1021/acs.analchem.6b01441.

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17

Safina, Galina. "Numerical solution of filtration in porous rock." E3S Web of Conferences 97 (2019): 05016. http://dx.doi.org/10.1051/e3sconf/20199705016.

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The filtration problem is one of the most relevant in the design of retaining hydraulic structures, water supply channels, drainage systems, in the drainage of the soil foundation, etc. Construction of transport tunnels and underground structures requires careful study of the soil properties and special work to prevent dangerous geological processes. The model of particle transport in the porous rock, which is based on the mechanical-geometric interaction of particles with a porous medium, is considered in the paper. The suspension particles pass freely through large pores and get stuck in small pores. The deposit concentration increases, the porosity and the permissible flow of particles through large pores changes. The model of one-dimensional filtration of a monodisperse suspension in a porous medium with variable porosity and fractional flow through accessible pores is determined by the quasi-linear equation of mass balance of suspended and retained particles and the kinetic equation of deposit growth. This complex system of differential equations has no explicit analytical solution. An equivalent differential equation is used in the paper. The solution of this equation by the characteristics method yields a system of integral equations. Integration of the resulting equations leads to a cumbersome system of transcendental equations, which has no explicit solution. The system is solved numerically at the nodes of a rectangular grid. All calculations are performed for non-linear filtration coefficients obtained experimentally. It is shown that the solution of the transcendental system of equations and the numerical solution of the original hyperbolic system of partial differential equations by the finite difference method are very close. The obtained solution can be used to analyze the results of laboratory research and to optimize the grout composition pumped into the porous soil.

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18

Kuzmina, Ludmila Ivanovna, and Yuri Viktorovich Osipov. "Asymptotic solution of the filtration equation." Vestnik MGSU, no. 2 (February 2016): 49–61. http://dx.doi.org/10.22227/1997-0935.2016.2.49-61.

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The problem of filtering a suspension of tiny solid particles in a porous medium is considered. The suspension with constant concentration of suspended particles at the filter inlet moves through the empty filter at a constant speed. There are no particles ahead of the front; behind the front of the fluid flow solid particles interact with the porous medium. The geometric model of filtration without effects caused by viscosity and electrostatic forces is considered. Solid particles in the suspension pass freely through large pores together with the fluid flow and are stuck in the pores that are smaller than the size of the particles. It is considered that one particle can clog only one small pore and vice versa. The precipitated particles form a fixed deposit increasing over time. The filtration problem is formed by the system of two quasi-linear differential equations in partial derivatives with respect to the concentrations of suspended and retained particles. The boundary conditions are set at the filter inlet and at the initial moment. At the concentration front the solution of the problem is discontinuous. By the method of potential the system of equations of the filtration problem is reduced to one equation with respect to the concentration of deposit with a boundary condition in integral form. An asymptotic solution of the filtration equation is constructed near the concentration front. The terms of the asymptotic expansions satisfy linear ordinary differential equations of the first order and are determined successively in an explicit form. For verification of the asymptotics the comparison with the known exact solutions is performed.

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19

Brunner, R., R. A. Widder, P. Walter, H. Borberg, and K. Oette. "Change in Hemorrheological and Biochemical Parameters following Membrane Differential Filtration." International Journal of Artificial Organs 18, no. 12 (1995): 794–98. http://dx.doi.org/10.1177/039139889501801208.

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Introduction: The elimination of high molecular weight proteins may have a positive influence on disorders of the microcirculation due to an improvement in rheological parameters. We therefore attempted to evaluate the rheological efficacy of membrane differential filtration (MDF). Patients and methods: Ten patients suffering from macular disease underwent MDF. Rheological and biochemical parameters as well as visual acuity were determined one day before and after therapy: The study aimed at a reduction in plasma viscosity, standardized whole blood viscosity at hematocrit 0.45 and erythrocyte aggregation at hematocrit 0.3. Results: Severe side-effects were not observed. The rheological parameters were significantly reduced. In detail the posttreatment values were reduced as compared to the pretreatment values as follows: plasma viscosity 85%, standardised whole blood viscosity 86% (hematocrit 0.45), erythrocyte aggregation 59% (hematocrit 0.3), total protein 81%, IgG 66%, IgA 59%, IgM 33%, alpha-2-macroglobulin 30%, triglycerides 102%, total cholesterol 47%, VLDL cholesterol 94%, LDL cholesterol 33%, HDL cholesterol 62%. Visual acuity was improved in 7/10 patients. Conclusions: MDF is a safe and highly effective method for lowering biochemical and improving rheological parameters which led to improvement in visual acuity. We have already replaced plasma exchange with MDF in our clinical practice of hemorrheological therapy.

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20

Lü, Qi, and Xu Zhang. "Well-posedness of backward stochastic differential equations with general filtration." Journal of Differential Equations 254, no. 8 (2013): 3200–3227. http://dx.doi.org/10.1016/j.jde.2013.01.010.

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21

Di Carlo, Dino, Jon F. Edd, Daniel Irimia, Ronald G. Tompkins, and Mehmet Toner. "Equilibrium Separation and Filtration of Particles Using Differential Inertial Focusing." Analytical Chemistry 80, no. 6 (2008): 2204–11. http://dx.doi.org/10.1021/ac702283m.

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22

Ravshanov, Normakhmad, Nozim Kurbonov, and Abduvali Mukhamadiev. "An Approximate Analytical Solution of the Problem of Fluid Filtration in the Multilayer Porous Medium." International Journal of Computational Methods 13, no. 06 (2016): 1650042. http://dx.doi.org/10.1142/s0219876216500420.

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This paper deals with a mathematical problem statement of unsteady fluid flow in heterogeneous porous media with various hydrogeological characteristics. In order to solve the problem the authors developed an approximate analytical method. The method allows multidimensional differential equation in partial derivatives describing the process of fluid filtration in layered porous media to become one-dimensional differential equation. There was obtained a calculation formula for determining the process of mass transfer between the layers, depending on the operating modes of production wells and hydrogeological parameters of filtration layers. The model and the algorithm can be used as a mathematical support for the processes of development of oil and gas fields.

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23

Agishi, T. "Selective Removal of Pathogenetic Macromolecules Directly from Whole Blood by Double Filtration Technique." International Journal of Artificial Organs 9, no. 5 (1986): 355–58. http://dx.doi.org/10.1177/039139888600900519.

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Double filtration plasmapheresis (DFPP) is a technique devised in an attempt to selectively remove pathogenetic macromolecules such as antibodies, immune complexes or viscosity-increasing substances directly from blood. In order to realize the differential filtration principle, two filters, one for separation of plasma and another for fractionation of plasma components, are installed in an extracorporeal circulation line. Selective separation of the plasma components is dependent on the filtration property of the two filters. Clinical experiences evidence the usefulness of this technique in regard to conservation of human blood products for supplementation.

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24

Mikishanina, E. A. "MODELING OF STEADY-STATE LIQUID FILTRATION IN A PIECEWISE INHOMOGENEOUS ELASTIC-POROUS MEDIUM IN THE CLASS OF ALMOST-PERIODIC FUNCTIONS (PLANE PROBLEM)." PNRPU Mechanics Bulletin, no. 2 (December 15, 2023): 38–46. http://dx.doi.org/10.15593/perm.mech/2023.2.05.

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When modeling liquid filtration in a porous medium, it is assumed that the filtration coefficient is constant, as a result of which the solution is simplified and reduced to a boundary value problem for the Laplace equation. In this paper, the almost periodic of Bohr analytical solutions of the plane problem of steady-state liquid filtration in an elastic – porous piecewise inhomogeneous domain are constructed using a generalized discrete Fourier transform . The domain is a strip consisting of several layers (strips) with different elastic and filtration parameters. Assuming that the filtration coefficient of an elastic-porous medium depends on the first invariant of the stress tensor, we consider it linearly dependent on the coordinate varying along the bandwidth. The filtration problem is reduced to solving a system of partial differential equations with specified boundary conditions on the upper and lower boundaries of the entire multilayer strip and conditions on the internal lines of the media interface, which in turn is reduced to solving the Cauchy problem for a system of Bessel ordinary differential equations. All solutions in this paper are obtained in the form of absolutely convergent Bohr-Fourier series, the coefficients of which are expressed in terms of given functions. Fluid filtration in a three-layer strip consisting of various light and sufficiently elastic-porous sedimentary and igneous rock layers is modeled. Graphs of the desired mechanical parameters are constructed. Their convergence to boundary conditions and conditions on the interface lines of media is shown. The paper also provides basic information concerning the properties of almost-periodic functions and the generalized discrete Fourier transform necessary for a more detailed understanding of the problem.

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25

Selivyorstova, Tatjana, Vadim Selivyorstov, and Yuliia Mala. "Fractional-differential approach to describe the process of feeding metals and alloys solidifying under controlled gas pressure." System technologies 4, no. 135 (2021): 149–55. http://dx.doi.org/10.34185/1562-9945-4-135-2021-15.

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To describe the processes of filtration in the folding dendritic-porous middle of the proponation, a number of fractional-differential mathematical models of the diffusion type. Described non-linear, how to take the shot of the abducted Riman-Leeuwill for an hour, as it can be stuck for a correct description of the single-phase filtration of not Newtonian age in the porous middle.The two-phase zone, which is established during the transition from melting from hard to hard mill, can often be characterized by abnormal kinetics of resistance. The peculiarities of kinetics in the whole range of winners are related to the issues of widespread nonlocality, in a number of types, memory defects, which adhere to the progressive laws. The mathe-?atical apparatus, which allows to adequately describe such processes, is the theory of integration-differentiation of the fractional order.Victorians in robotic thinking have a phenomenological character, so the possibility of their dependence in a specific, practical dermal condition is blamed on the basis of experimental results, so that the validity of other differences is confirmed. Stagnation of the given approach for describing the dynamics of the process of vitality of the two-phase zones and metals and alloys, which solidifies in the minds of a regulated gas vice. Presented in the fractional-differential robotic model of filtration are classified as abnormal diffusion. A characteristic feature of the ryvnyan, which is derived from different types of differential models of filtration, is not the same. With a whole model, they preserve the structure of the classical lines of filtration in the whole order and pass into them in boundary drops, if the order of the other differentiation is old.Vivchennya yakіsnyh authorities otrimanih іvnyans, and also prompts їh numerical decisions є to finish nontrivial zavdannyi, as vimagayut in the skin okremomu vampad of independent thought.

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26

Shagapov, V. Sh, and Z. M. Nagaeva. "On elastic regime of filtration in hydraulic fracture." Proceedings of the Mavlyutov Institute of Mechanics 11, no. 2 (2016): 156–66. http://dx.doi.org/10.21662/uim2016.2.023.

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Fluid recovery from a well in the modes of constant pressure drop and constant flow rate is considered basing on a theoretical model of filtration in a hydraulic fracture. Exact analytical solutions are obtained that allowed analyzing the effect of the reservoir and fracture properties (such as porosity, permeability and crack width) as well as the rheological properties of the saturating fluid upon: pressure evolution in the fracture, well flow rate at constant pressure drop, and pressure evolution in the wellbore. On the basis of theoretical models describing the filtration for a crack in an oil or gas reservoirs, the considered problem on the selection of fluids from the well in modes constant differential pressure and constant flow. For the considered tasks are received exact analytical solutions, based on which we analyzed the influence of reservoir characteristics of the formation and fractures (for example, their porosity, permeability and width of cracks) and the rheological properties of the saturating fluid on the evolution of the pressure in the fracture, the production rate at a constant differential to the dynamics of the pressure in the well.

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27

Freeman, Charles, Reuben Burch, Lesley Strawderman, et al. "Do They Really Work? Quantifying Fabric Mask Effectiveness to Improve Public Health Messaging." International Journal of Environmental Research and Public Health 19, no. 11 (2022): 6372. http://dx.doi.org/10.3390/ijerph19116372.

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The purpose of this study is to compare masks (non-medical/fabric, surgical, and N95 respirators) on filtration efficiency, differential pressure, and leakage with the goal of providing evidence to improve public health messaging. Masks were tested on an anthropometric face filtration mount, comparing both sealed and unsealed. Overall, surgical and N95 respirators provided significantly higher filtration efficiency (FE) and differential pressure (dP). Leakage comparisons are one of the most significant factors in mask efficiency. Higher weight and thicker fabric masks had significantly higher filtration efficiency. The findings of this study have important implications for communication and education regarding the use of masks to prevent the spread of COVID-19 and other respiratory illnesses, specifically the differences between sealed and unsealed masks. The type and fabric of facial masks and whether a mask is sealed or unsealed has a significant impact on the effectiveness of a mask. Findings related to differences between sealed and unsealed masks are of critical importance for health care workers. If a mask is not completely sealed around the edges of the wearer, FE for this personal protective equipment is misrepresented and may create a false sense of security. These results can inform efforts to educate health care workers and the public on the importance of proper mask fit.

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Daliev, Sherzod, Fazliddin Sirojiddinov, and Oxun Khaitov. "Developing Mathematical Models to Study Changes in Groundwater Levels and Salt Concentration." E3S Web of Conferences 589 (2024): 03011. http://dx.doi.org/10.1051/e3sconf/202458903011.

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Understanding how groundwater and salt concentrations change when freshwater supplies are monitored is crucial. In this work, groundwater fluxes and salt migration were considered when studying groundwater level changes and mineralisation processes. To study salt and water level changes, a more realistic mathematical model was developed to reflect the object’s basic features. To monitor geofiltration and geomigration using mathematical and numerical modelling to provide recommendations, nonlinear differential equations were applied. Scientific research on mathematical and numerical modelling and computer experimentation of the issue is briefly reviewed. Also developed were a mathematical model with two integer-valued boundary conditions and an efficient finite difference numerical approach. Changing groundwater and pressure water levels, filtration permeability, water loss coefficient, and filtration rate connected to water level all affect the environment when building a mathematical model for salt migration filtration. The article predicts groundwater, pore water, and salt concentrations in high- and low- permeability layers. Scientific research on mathematical and numerical modelling and computer experimentation of the issue is briefly reviewed. Also developed were a mathematical model with two integer-valued boundary conditions and an efficient finite difference numerical approach. Changing groundwater and pressure water levels, filtration permeability, water loss coefficient, and filtration rate connected to water level all affect the environment when building a mathematical model for salt migration filtration. This study considered soil density, active porosity, and third-order boundary conditions Open, unlike earlier studies. Since the problem is represented by nonlinear differential equations with free variables, analytical solutions are unattainable. An effective numerical method and a stable implicit system with high-accuracy approximation, finite difference approach, and forward and backward sweep approaches were given to overcome these challenges.

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Santos, Nathalia Fontes de Souto dos, Vanessa Viscardi, Anna Clara Porthun Caruso, Rodolpho de Almeida Torres Filho, Nayro Xavier de Alencar, and Daniel Augusto Barroso Lessa. "EQUINE TRACHEOBRONCHIAL WASH FILTRATION AND ITS EFFECTS ON DIFFERENTIAL CELL COUNT." Ciência Animal Brasileira 17, no. 2 (2016): 274–78. http://dx.doi.org/10.1590/1089-6891v17i231988.

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Abstract Tracheobronchial wash (TBW) is a method to recover cell samples from the airways. The cytology of TBW fluid is an important technique for the diagnosis of pulmonary diseases in horses. Excessive mucus in TBW may cause cell damage and morphological changes that hinder cell type recognition, resulting in a misdiagnosis. The aim of this study was to compare the results of differential cell count in a tracheobronchial wash of filtered and non-filtered samples. Endoscopy and TBW procedures were performed in thirty horses. Each TBW sample was split into two aliquots. Two groups were formed: non-filtrated aliquots (NF) and filtrated aliquots (F). The filtration was performed using a hydrophilic gauze pad. After centrifugation, the differential cell count was performed considering 300 nucleated cells. The filtrated aliquots results presented a significant increase of macrophages count and a significant decrease in neutrophils count comparing to the results of non-filtrated aliquots. These findings were consistent with results of filtered bronchoalveolar wash published studies. Therefore, the filtration of TBW is not an efficient method.

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Gard, M. F. "Measurement of X-ray tube accelerating potential by differential beam filtration." IEEE Transactions on Instrumentation and Measurement 45, no. 3 (1996): 745–49. http://dx.doi.org/10.1109/19.494592.

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Zhu, Minxian. "A Weyl module filtration for the vertex algebra of differential operators." Representation Theory of the American Mathematical Society 15, no. 10 (2011): 370. http://dx.doi.org/10.1090/s1088-4165-2011-00381-2.

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Nordén, Harry V., and Petteri Kauppinen. "Application of Volume Balances and the Differential Diffusion Equation to Filtration." Separation Science and Technology 29, no. 10 (1994): 1319–34. http://dx.doi.org/10.1080/01496399408006943.

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33

Lüke, C., R. A. Widder, F. Soudavar, P. Walter, R. Brunner, and H. Borberg. "Improvement of macular function by membrane differential filtration in diabetic retinopathy." Journal of Clinical Apheresis 16, no. 1 (2001): 23–28. http://dx.doi.org/10.1002/jca.1004.

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Chen, Qiqi, Yujian Liu, Hangjun Deng, et al. "Melt differential electrospinning of polyphenylene sulfide nanofibers for flue gas filtration." Polymer Engineering & Science 60, no. 11 (2020): 2887–94. http://dx.doi.org/10.1002/pen.25520.

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Bondarko, M. V. "Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura." Journal of the Institute of Mathematics of Jussieu 8, no. 1 (2008): 39–97. http://dx.doi.org/10.1017/s147474800800011x.

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AbstractWe describe explicitly the Voevodsky's triangulated category of motives $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$ (and give a ‘differential graded enhancement’ of it). This enables us to able to verify that DMgm ℚ is (anti)isomorphic to Hanamura's $\mathcal{D}$(k).We obtain a description of all subcategories (including those of Tate motives) and of all localizations of $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$. We construct a conservative weight complex functor $t:\smash{\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}}\to\smash{K^{\mathrm{b}}(\operatorname{Chow}^{\mathrm{eff}})}$; t gives an isomorphism $K_0(\smash{\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}})\to\smash{K_0(\operatorname{Chow}^{\mathrm{eff}})}$. A motif is mixed Tate whenever its weight complex is. Over finite fields the Beilinson–Parshin conjecture holds if and only if tℚ is an equivalence.For a realization D of $\operatorname{DM}^{\mathrm{eff}}_{\mathrm{gm}}$ we construct a spectral sequence S (the spectral sequence of motivic descent) converging to the cohomology of an arbitrary motif X. S is ‘motivically functorial’; it gives a canonical functorial weight filtration on the cohomology of D(X). For the ‘standard’ realizations this filtration coincides with the usual one (up to a shift of indices). For the motivic cohomology this weight filtration is non-trivial and appears to be quite new.We define the (rational) length of a motif M; modulo certain ‘standard’ conjectures this length coincides with the maximal length of the weight filtration of the singular cohomology of M.

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Аlexeev, B. V. "ANALYTIC SOLUTION OF NONLINEAR LEYBENSON EQUATION IN THE THEORY OF FILTRATION." Fine Chemical Technologies 11, no. 1 (2016): 34–39. http://dx.doi.org/10.32362/2410-6593-2016-11-34-39.

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Analytic solution of nonlinear Leybenson equation in the theory of filtration is obtained. Analytical solutions of the partial differential equations are presented in the explicit algebraic form. The integral surfaces in three dimensions are presented.

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37

Benz, Nikolai, Fabian Krull, Kai Nikolaus, and Sergiy Antonyuk. "Membrane–Fabric Composite Filter Media for Continuous Cake Filtration without Gas Throughput Using Paste Dot Coating with Adhesive." Membranes 13, no. 9 (2023): 801. http://dx.doi.org/10.3390/membranes13090801.

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In the field of liquid filtration, the realization of gas throughput-free cake filtration has been investigated for a long time. Cake filtration without gas throughput would lead to energy savings in general and would reduce the mechanically achievable residual moisture in filter cakes in particular. The reason why gas throughput-free filtration could not be realized with fabrics so far is that the achievable pore sizes are not small enough, and that the associated capillary pressure is too low for gas throughput-free filtration. Microporous membranes can prevent gas flow through open pores and cracks in the filter cake at a standard differential pressure for cake filtration of 0.8 bar due to their smaller pore size. Since large-scale implementation with membranes was not yet successful due to their inadequate mechanical strength, this work focuses on the development and testing of a novel composite material. It combines the advantages of gas throughput-free filtration using membranes with the mechanical stability of fabrics. For the production of the composites, a paste dot coating with adhesive, which is a common method in the textile industry, was used. Based on filtration experiments, delamination and tensile tests, as well as µCT analysis, it is shown that this method is suitable for the production of composite filter materials for gas throughput-free cake filtration.

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CORNEA, O., K. A. DE REZENDE, and M. R. DA SILVEIRA. "Spectral sequences in Conley’s theory." Ergodic Theory and Dynamical Systems 30, no. 4 (2009): 1009–54. http://dx.doi.org/10.1017/s0143385709000479.

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AbstractIn this paper, we analyse the dynamics encoded in the spectral sequence (Er,dr) associated with certain Conley theory connection maps in the presence of an ‘action’ type filtration. More specifically, we present an algorithm for finding a chain complex C and its differential; the method uses a connection matrix Δ to provide a system that spans Er in terms of the original basis of C and to identify all of the differentials drp:Erp→Erp−r. In exploring the dynamical implications of a non-zero differential, we prove the existence of a path that joins the singularities generating E0p and E0p−r in the case where a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow, and proves to be important in some applications.

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KAPLUNOV, D. R., A. N. KACHURIN, G. V. FRIDLENDER, and M. P. GANIN. "CALCULATING FILTRATION AIR FLOW IN THE BLOCK OF GASIFIED COAL BED." News of the Tula state university. Sciences of Earth 2, no. 1 (2020): 283–89. http://dx.doi.org/10.46689/2218-5194-2020-2-1-283-289.

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The mathematical model for calculating the filtration air flow in the block of gasified coal bed is substantiated. It is proved that the rate of filtration of the air flow in the block of gasified coal bed will depend on the gas permeability of coal and the difference between the squares of the air pressure on the lines of injection and production wells. It is shown that the filtration rate of the air flow in the block of gasified coal bed is one of the main physical parameters of the process of underground coal gasification. Obviously, the efficiency of underground coal gasification can be controlled by changing the rate of filtration of the air flow, by changing the gas permeability of the coal bed and the differential pressure of air on the lines of injection and production wells.

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Krupp, A. U., I. M. Griffiths, and C. P. Please. "Stochastic modelling of membrane filtration." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (2017): 20160948. http://dx.doi.org/10.1098/rspa.2016.0948.

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Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances and deposition on the membrane surface. In this paper, we present an efficient method for modelling the behaviour of a filter, which accounts for different retention mechanisms, particle sizes and membrane geometries. The membrane is assumed to be composed of a series of, possibly interconnected, pores. The central feature is a conductivity function , which describes the blockage of each individual pore as particles arrive, which is coupled with a mechanism to account for the stochastic nature of the arrival times of particles at the pore. The result is a system of ordinary differential equations based on the pore-level interactions. We demonstrate how our model can accurately describe a wide range of filtration scenarios. Specifically, we consider a case where blocking via multiple mechanisms can occur simultaneously, which have previously required the study through individual models; the filtration of a combination of small and large particles by a track-etched membrane and particle separation using interconnected pore networks. The model is significantly faster than comparable stochastic simulations for small networks, enabling its use as a tool for efficient future simulations.

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KEDLAYA, KIRAN S. "LOCAL MONODROMY OF p-ADIC DIFFERENTIAL EQUATIONS: AN OVERVIEW." International Journal of Number Theory 01, no. 01 (2005): 109–54. http://dx.doi.org/10.1142/s179304210500008x.

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This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda's classification of quasi-unipotent ∇-modules, the Christol–Mebkhout construction of the ramification filtration, and the Christol–Dwork Frobenius antecedent theorem. We also briefly discuss the p-adic local monodromy theorem without proof.

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Alimbekova, N. B., D. R. Baigereyev, and M. N. Madiyarov. "Study of a Numerical Method for Solving a Boundary Value Problem for a Differential Equation with a Fractional Time Derivative." Izvestiya of Altai State University, no. 4(114) (September 9, 2020): 64–69. http://dx.doi.org/10.14258/izvasu(2020)4-10.

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Recently, there has been an increased interest in the problem of numerical implementation of multiphase filtration models due to its enormous economic importance in the oil industry, hydrology, and nuclear waste management. In contrast to the classical models of filtration, filtration models in highly porous fractured formations with the fractal geometry of wells are not fully understood. The solution to this problem reduces to solving a system of differential equations with fractional derivatives. In the paper, a finite-difference scheme is constructed for solving the initial-boundary value problem for the convection-diffusion equation with a fractional time derivative in the sense of Caputo-Fabrizio. A priori estimates are obtained for solving a difference problem under the assumption that there is a solution to the problem in the class of sufficiently smooth functions that prove the uniqueness of the solution and the stability of the difference scheme. The convergence of the solution of the difference problem to the solution of the original differential problem with the second order in time and space variables is shown. The results of computational experiments confirming the reliability of theoretical analysis are presented.

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Gülle, Saniye, Mustafa Bak, Erkin Serdaroglu, Demet Can, and Ozalp Karabay. "Low-Density Lipoprotein Apheresis by Membrane Differential Filtration (Cascade Filtration) via Arteriovenous Fistula Performed in Children With Familial Hypercholesterolemia." Therapeutic Apheresis and Dialysis 14, no. 1 (2010): 87–92. http://dx.doi.org/10.1111/j.1744-9987.2009.00795.x.

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Li, Yan Xia, Hao Hu, Mao Zhong Hu, Liang Yin, Dan Yang, and Shi Qiu. "Air Filtration and Pressure Boost Technique for the Operating Room of Construction Machinery." Advanced Materials Research 468-471 (February 2012): 168–72. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.168.

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An air filtration and pressure boost technique for the operating room was brought forward to the construction machinery working in dust atmosphere. The constitution, rationale and design method of the air filtration and pressure boost system was introduced in details. The method was successfully used to the operating room upgrade for a small scoop-tram. A certain positive pressure differential was maintained between the upgraded operating room and the outside, which preventing the access of the outside dust to the interior room and protecting the operator.

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Sandrakov, G. V. "COMPUTATIONAL ALGORITHMS FOR MULTIPHASE HYDRODYNAMICS MODELS AND FILTRATION." Journal of Numerical and Applied Mathematics, no. 1 (2022): 46–61. http://dx.doi.org/10.17721/2706-9699.2022.1.04.

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Computational algorithms for modeling of multiphase hydrodynamics processes with take of phase transitions will be discussed. The algorithms are based on discretization of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial discretization is natural and numerical simulations are realized as direct computer experiments. The experiments are implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite–diamond phase transitions and calculations are given. Modification of the algorithms have also been developed to take into account the influence of viscosity when simulating the dynamics of a multiphase fluid in porous media.

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QADERMARZI, AMIR, MOJTABA POULADI, ALI REZAMAND, SEYED HOSSEIN HOSEINIFAR, and ALI AKBAR HEDAYATI. "Investigation of sub-acute levels of zinc oxide nanoparticles on the filtration rate of Mytilaster lineatus and Dressina polymorpha in the short term." Nusantara Bioscience 10, no. 1 (2018): 53–57. http://dx.doi.org/10.13057/nusbiosci/n100108.

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Qadermarzi A, Pouladi M, Rezamand A, Hoseinifar SH, Hedayati AA. 2018. Investigation of sub-acute levels of zinc oxide nanoparticles on the filtration rate of Mytilaster lineatus and Dressina polymorpha in the short term. Nusantara Bioscience 10: 53-57. The filtration rate is one of the physiological indices in the bivalves which indicate the degree of efficacy of the filtration function in the exposure to contaminants. In this study, changes in the filtration rate of freshwater bivalves (D. polymorpha and M. lineatus) were investigated after exposure periods of 5 and 10 days with nanoparticles. Bivalves were transferred from the natural environment to the laboratory. The distribution of nanoparticles was measured by differential light scattering (DLS). Bivalves were exposed to 2.5, 25 and 50 ppm nanoparticles for ten days in water reservoirs. The filtration rates were significantly different in the treatments compared to the control samples, with the highest filtration rate was observed in the control group. On the fifth day, the highest filtration rate was obtained in the first treatment of M. lineatus and the lowest filtration rate was obtained in the third treatment of D. polymorphia. The highest filtration rates were observed in the first and second treatments and the lowest filtration rate was observed in the third treatment. Also, there was no significant difference in the filtration rate of M. lineatus in the 1st treatment with control (P> 0.05) on the 5th day, but filtration rate was significantly (P <0.05) less than other concentrations and control group in the third treatment. On the other hand, the filtration rates on the 10th day showed similar differences compared to the 5th day. It could be concluded that the changes infiltration rate are an appropriate indicator for the measurement of contamination in nanoparticles.

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Aigerim T. Rakhymova, Mars B. Gabbassov, and Anvarjon A. Ahmedov. "Analytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 1 (2021): 118–33. http://dx.doi.org/10.37934/arfmts.87.1.118133.

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This paper is devoted to the study of the Cauchy problem for a system of differential equations describing the unsteady flow of a compressible fluid in a homogeneous and inhomogeneous porous medium with a general nonlinear filtration law in three-dimensional space. In the work using the methods of four-dimensional mathematics, a special four-dimensional space of space and time coordinates was developed, as well as a functional space of regular functions, and analytical conditions were obtained on the general form of the nonlinear filtration law for which the Cauchy problem has a solution.

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FAIDI, WAHID, ANIS MATOUSSI, and MOHAMED MNIF. "OPTIMAL STOCHASTIC CONTROL PROBLEM UNDER MODEL UNCERTAINTY WITH NONENTROPY PENALTY." International Journal of Theoretical and Applied Finance 20, no. 03 (2017): 1750015. http://dx.doi.org/10.1142/s0219024917500157.

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In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type [Formula: see text]-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty is studied in the context of a Brownian filtration. In the case of consistent time penalty, we characterize the value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounded terminal condition.

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Nagase, Youichi, Kenji Okada, and Shaoxiang Qian. "Constitutive Equation and Governing Differential Equation for Filtration Expressed in Moving Coordinate." Journal of the Society of Powder Technology, Japan 40, no. 10 (2003): 712–19. http://dx.doi.org/10.4164/sptj.40.712.

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Bogaenko, V. A., and V. M. Bulavatsky. "Computer modeling of the fractional-differential dynamics of some filtration-consolidation processes." Reports of the National Academy of Sciences of Ukraine, no. 4 (April 28, 2018): 16–24. http://dx.doi.org/10.15407/dopovidi2018.04.016.

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