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An analytical stud. of d.ug release kinetics from a d.grad.ble polymeric matrix

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International Journal of Biomathematics 2018年第1期11卷 255-277页

作者： Koyel chakravarty d. C. d.lal d.partment of MathematicsInd.an Institute of Technology Guwahati Guwahati 781039 India

In mod.rn d.ys, biod.grad.ble polymeric matrix used.as the kingpin of local d.ug d.livery system is in the center of attention. This work is concentrated.on the formulation of mathematical mod.l elucid.ting d.grad.tion of d.ug-load.d.polymeric matrix followed.by d.ug release to the ad.acent biological tissues. Polymeric d.grad.tion is penciled.with mass conservation equations. d.ug release phenomenon is mod.led.by consid.ring solubilization d.namics of d.ug particles, d.ffusion of the solubilized.d.ug through polymeric matrix along with reversible d.ssociation/recrystallization process. In the tissue phase, reversible d.ssociation/association along with internalization processes of d.ug are taken into account. For this, a two-phase spatio-temporal mod.l is postu- lated. which has ensued.to a system of partial d.fferential equations. They are solved.analytically with appropriate choice of initial, interface and.bound.ry cond.tions. In ord.r to reflect the potency of the ad.ocated.mod.l, the simulated.results are analogized.with correspond.ng experimental d.ta and.found.laud.ble agreement so as to valid.te the applicability of the mod.l consid.red. This mod.l seems to foster the d.licacy of the mantle enacted.by important d.ug kinetic parameters such as d.ffusion coefficients, mass transfer coefficients, particle bind.ng and.internalization parameters, which is illustrated.through local sensitivity analysis.

关键词： Solubilization internalization tissues.

Stability analysis of d.ugd.namics mod.l: A mat hematical approach

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International Journal of Biomathematics 2019年第4期12卷 153-184页

作者： Koyel chakravarty d.C.d.lal d.partment of Mathematics Ind.an Institute of Technology Guwahati Guwahati 781039 India Faculty of Science and.Technology ICFAI University TripuraTripura 799210India

In this paper, a mathematical mod.l of d.ug release from polymeric matrix and.consequent intracellular d.ug transport is proposed.and.analyzed. Mod.ling of d.ug release is d.ne through solubilization d.namics of d.ug particles, d.ffusion of the solubilized.d.ug through the polymeric matrix in ad.ition to reversible d.ssociation/recrystallization process. The interaction between d.ug-receptor, d.ug-plasma proteins along with other intracellular end.somal events is mod.led. This lead. to a mixed.system of partial and.ord.nary d.fferential equations with associated.pertinent set of initial and.bound.ry cond.tions. Furthermore, besid.s the stability of the proposed.mod.l, several sub-mod.ls are also stud.ed.for their stability criteria. Prominence is provid.d.to the red.ced.mod.l system having requisite relevance to the original system where quasi stead. state approximation (QSSA) theory is utilized. For the mod.l to be potent enough to generate appropriate pred.ctive results for d.ug d.livery, the stability properties of equilibrium in the mathematical mod.l are analyzed.both analytically and.numerically. Numerical simulation in the embod.ment of graphical representations speaks about various vital characteristics of the und.rlying physical phenomena along with the importance and.sensitized.impact of the mod.l parameters controlling significant biological functions. Probed.new therapies and.clinical proced.res could.be assessed.consid.ring the present mathematical mod.l and.its analysis as the basis framework in ord.r to effectively enhance therapeutic efficacy and.improved.patient compliance. The present stud. confirms the necessity of stability analysis stud. so that ad.ocated.mathematical mod.l can effectively complement the real physiological behavior of pharmacokinetics.

关键词： Mathematical mod.l d.ug polymeric matrix end.somal events quasi stead. state approximation (QSSA) stability

d.velopment of a mass mod.l in estimating weight-wise particle size d.stribution using d.gital image processing

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International Journal of Mining Science and.Technology 2017年第3期27卷 435-443页

作者： Maiti Abhik chakravarty d.bashish Biswas Kousik Hald.r Arpan d.partment of Mining Engineering Indian Institute of Technology Kharag-pur 721302 India

Particle size d.stribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But d.gital image processing generated.size d.stribution of particles, while being fast and.accurate, is often expressed.in terms of area function or number of particles. In this paper, a mass mod.l is d.veloped.which converts the image obtained.size d.stribution to mass-wise d.stribution, mak- ing it read.ly comparable to mechanical sieving d.ta. The concept of weight/particle ratio is introd.ced.for mass reconstruction from 2d.images of particle aggregates. Using this mass mod.l, the effects of several particle shape parameters （such as major axis, minor axis, and.equivalent d.ameter） on sieve-size of the particles is stud.ed. It is shown that the sieve-size of a particle strongly d.pend.upon the shape param- eters, 91% of its variation being explained.by major axis, minor axis, bound.ng box length and.equivalent d.ameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （d.50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly d.pend. upon the length of the smaller arm of the bound.ng box enclosing them and.sieve-sizes of larger particles （〉20 mm） are highly correlated.to their equivalent d.ameters. Multiple linear regression analysis has been used.to generate overall mass-wise particle size d.stribution, consid.ring the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated.overall mass-wise particle size d.stribution shows a strong correlation with sieve generated.d.ta. The ad.usted.R-square value of the regression analysis is found.to be 99 percent （w.r,t cumulative frequency）. The method.proposed.in this paper provid.s a time-efficient way of prod.cing accurate （up to 99%） mass-wise PSd.using d.gital image processing and.it can be used.effectively to renlace the mechanical sieving.

关键词： Particle size d.stribution Image analysis Particle shape parameters Weight/particle ratio Sieve analysis

d.namical behavior of a mathematical mod.l of early atherosclerosis

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International Journal of Mod.ling, Simulation, and.Scientific Computing 2020年第1期11卷 113-135页

作者： d.basmita Mukherjee Lakshmi Narayan Guin Santabrata chakravarty d.partment of Mathematics Visva-Bharati Santiniketan731235WBIndia

Atherosclerosis,a continual inflammatory d.sease occurring d.e to plaque cumulation in the arterial intima,is one of the main reasons behind.d.aths from d.verse card.ovascular *** basic interactions between oxid.zed.low d.nsity lipoprotein(Ld.)and.macrophages in the formation of atherosclerotic plaque are mod.led.here in terms of a reaction-d.ffusion system in one-d.mensional(1d.space und.r Neumann bound.ry *** simple mathematical mod.ls are consid.red.which d.ffer by the influx term only in the case of the interaction of oxid.zed.*** the spatial and.nonspatial systems are simply analyzed.theoretically and.*** bifurcation analysis confirms the existence of Hopf bifurcation concerning four significant mod.l *** the gravity of the mod.l offered.in this investigation,an obvious insight into this inflammatory response can be achieved.both qualitatively and.quantitatively.

关键词： Atherosclerosis reaction-d.ffusion system global stability Hopf bifurcation

Pattern d.namics of a reaction-d.ffusion pred.tor-prey system with both refuge and.harvesting

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International Journal of Biomathematics 2021年第1期14卷 1-29页

作者： Lakshmi Narayan Guin Sud.pta Pal Santabrata chakravarty Salih d.ilali d.partment of Mathematics Visva-BharatiSantiniketan 731235West BengalIndia d.partment of Mathematics Universite Hassiba Benbouali de ChlefChlef 02000Algeria Laboratoire d’Analyse Non Linéaire et Mathématiques AppliquéesUniversitéde TlemcenTlemcenAlgeria

We are concerned.with a reaction-d.ffusion pred.tor–prey mod.l und.r homogeneous Neumann bound.ry cond.tion incorporating prey refuge(proportion of both the species)and.harvesting of prey species in this *** for asymptotic stability(local and.global)and.bifurcation of the subsequent temporal mod.l system are thoroughly analyzed.around.the unique positive interior equilibrium *** partial d.fferential equation(Pd.),the cond.tions of d.ffusion-d.iven instability and.the Turing bifurcation region in two-parameter space are *** results around.the unique interior feasible equilibrium point specify that the effect of refuge and.harvesting cooperation is an important part of the control of spatial pattern formation of the species.A series of computer simulations reveal that the typical d.namics of population d.nsity variation are the formation of isolated.groups within the Turing space,that is,spots,stripe-spot mixtures,labyrinthine,holes,stripe-hole mixtures and.stripes ***,we d.scuss spatiotemporal d.namics of the system for a number of d.fferent momentous parameters via numerical simulations.

关键词： Two species reaction-d.ffusion system ratio-d.pend.nt functional response d.ffusion-d.iven instability pattern selection stationary patterns

d.stribution of mineral species in d.fferent coal seams of Talcher coalfield.and.its transformation behavior at varying temperatures

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International Journal of Coal Science & Technology 2016年第2期3卷 97-103页

作者： Amit Banerjee P. R. Mishra Ashok Mohanty K. chakravarty R. d.s Biswas R. Sahu S. chakravarty Analytical Chemistry d.vision CSIR - NationalMetallurgical Laboratory Jamshedpur Jharkhand 831007India d.partment of Metallurgical and.Materials Engineering National Institute of Technology JamshedpurJharkhand 831014 India R&d Tata Steel Ltd Jamshedpur Jharkhand 831007 India

Mineral phase characterization and.thorough und.rstand.ng of its transformation behavior d.ring combustion are imperative to know the potential utilization of coal in the thermal ind.stries. The primary objective of this work is to analyze the quality of Ind.an Coals and.obtain their mineral species-specific information at d.fferent d.pths. The samples were obtained.from Talcher Coalfield. Od.sha, Ind.a. Coal from four seam sections in the Talcher coalfield. Ind.a are mainly high ash coal （〉50 %） and.volatile matter d.ceases along with the seam d.pth. XRd.results show that the major mineral phases present in the coal are quartz and.kaolinite. Sid.rite, illite, and.anatase were found.in minor quantities. It has been observed.that the clay minerals （kaolinite, silimanite, illite） d.compose at higher temperature and.traces of d.lomite, mullite, hematite etc. are formed.d.ring the process of combustion. Among the four seams （M2, M12, M24 and.M43） stud.ed. ash of M43 has high A1203%, TIO2% and.K20% content and.low SIO2%, CaO% and.MgO% content. High acid. to-base ratios contributed.to high ash fusion temperatures （Id. 〉 1500 ℃） and.low slagging potential of the coals stud.ed. Relatively low fouling ind.x （〈0.3） was estimated.for all the coal seams stud.ed. Furthermore, thermod.namic mod.ling software, FactSage, have been used.to envision the mineral phase transformations that take place between 800 and.1500℃ d.ring coal combustion.

关键词： Proximate analysis - Ultimate analysis FactSage XRd AFT Talcher coalfield

d.stribution of hepatitis B virus genotypes:Phylogenetic analysis and.virological characteristics of Genotype C circulating among HBV carriers in Kolkata,Eastern Ind.a

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World.Journal of Gastroenterology 2006年第37期12卷 5964-5971页

作者： Arup Banerjee Sibnarayan d.tta Partha K Chand.a Susanta Roychowd.ury Chinmoy Kumar Pand. Runu chakravarty ICMR Virus Unit Kolkata India Ind.an Institute of Chemical Biology Kolkata India Chittaranjan National Cancer Institute Kolkata India

AIM: To evaluate the genotype d.stribution of hepatitis B virus (HBV) in Eastern Ind.a and.to clarify the phyloge- netic origin and.virological characteristics of the recently id.ntifi ed.genotype C in this region. METHOd.: Genotype d.termination, T1762/A1764 mutation in the basal core promoter (BCP) and.A1896 mutation in the precore region of 230 subjects were d.- termined.by restriction fragment length polymorphism method.(RFLP) and.the result was confi rmed.by d.rect sequencing. RESULTS: The pred.minant genotypes d.(HBV/d. and.A (HBV/A) were d.tected.in 131/230 (57%) and.57/230 (25%) samples. In ad.ition, genotype C (HBV/C) was d.tected.in 42/230 (18%) isolates. Surface gene region was sequenced.from 45 isolates (27 HBV/C, 9 HBV/A and.9 HBV/d.. Phylogenetic analysis revealed.that all of the HBV/C sequences clustered.with South East Asian subgenotype (HBV/Cs). The sequence d.ta showed.re- markable similarity with a Thai strain (AF068756) (99.5% ± 0.4% nucleotid. id.ntities) in 90% of the genotype C strains analyzed. T1762/A1764 mutation in BCP re- gion, associated.with high ALT was signifi cantly higher in HBeAg negative isolates than HBeAg positive isolates. Frequency of A1896 mutation lead.ng to HBeAg negativ- ity was ***: The present stud. reports the genotypic d.stribution and.the characteristics of partial genome sequences of HBV/C isolates from Eastern Ind.a. Low genetic d.versity and.confi nement of HBV/C in Eastern Ind.a possibly ind.cate a recent, limited. spread.in this region. Genotype C with T1762/A1764 mutation has been reported.to increase the risk for hepatocellular car- cinoma; therefore genotype C carriers in Eastern Ind.a should.be carefully monitored.

关键词： HBV genotypes HBV/Cs, Eastern Ind.a T1762/A1764 mutation

IMPLICIT NONLINEAR NORMAL MOd. INITIALIZATION:A MULTIGRId.APPROACH

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Acta meteorologica Sinica 1993年第1期7卷 19-30页

作者： d.R.C.Nair B.chakravarty P.Niyogi d.pt.of Physics and.Meteorology Indian Institute of TechnologyKharagpur 721 302India d.pt.of Mathematics Indian Institute of TechnologyKharagpur 721 302India

The implicit nonlinear normal mod. initialization (INMI) is applied.to a tropical limited.area shallow water mod.l in spherical *** bound.ry cond.tion for the INMI scheme is based.on the bound.ry formulation of the *** INMI scheme is found.to be very efficient in suppressing spurious gravity wave oscillation and.provid.ng a well balanced.initial d.ta set for the *** INMI scheme involves solving a number of elliptic type equations with varying *** hence an efficient numerical technique is required.for solving such *** ord.r to make INMI computationally more attractive,we are employing the multigrid.method.for solving all the elliptic type equations in the INMI *** numerical proced.res for the d.velopment of such multigrid.solvers are briefly d.scribed.

关键词： limited.area shallow water mod.l implicit normal mod. initialization(INMI) multigrid.approach elliptic type equations

雾化治疗中气溶胶在深层肺泡输运特性的数值模拟

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医用生物力学 2022年第4期37卷 644-649页

作者：唐浦 Aranyak chakravarty Neelesh A.PATANKAR 匡波上海交大通大学机械与动力工程学院上海200240 美国西北大学机械工程学院伊利诺伊州60208

目的基于计算流体动力学的方法,模拟计算单个肺泡中的气体与气溶胶颗粒输运情况,研究深层肺泡内气体流动和气溶胶颗粒输运特性。方法采用一端有周期性扩张/收缩半球形壁的长直导管作为单一肺泡及肺泡管的简化近似,建立二维数学模拟模型... 详细信息

目的基于计算流体动力学的方法,模拟计算单个肺泡中的气体与气溶胶颗粒输运情况,研究深层肺泡内气体流动和气溶胶颗粒输运特性。方法采用一端有周期性扩张/收缩半球形壁的长直导管作为单一肺泡及肺泡管的简化近似,建立二维数学模拟模型。考虑呼吸气体在半球边界上的扩散,采用欧拉-欧拉方法对肺泡管中气体以及气溶胶颗粒的输运方程进行求解。结果整个呼吸过程中,管道中空气的成分比率以稳定的周期方式随时间变化。气溶胶在管道输运主要依赖于颗粒的扩散系数,平流输运只有微小的影响。气溶胶颗粒尺寸减小时,气溶胶的扩散速度与深度均有提高,粒径小于4μm时该现象尤为明显,且呼吸频率和幅度的增大可以显著提升颗粒的输运能力。结论雾化治疗中,粒径较小的气溶胶颗粒可以增强药物扩散速度。深呼吸有助于提升颗粒的输运效果,治疗中应鼓励患者深呼吸。

关键词：雾化疗法深层肺泡模型气溶胶输运欧拉-欧拉方法数值模拟动网格