DigiLoCS: A leap forward in predictive organ-on-chip simulations. by Manoja Rajalakshmi Aravindakshan, Chittaranjan Mandal, Alex Pothen, Stephan Schaller, Christian Maass

“…Our approach involves the creation of a compartmental physiological model of the liver using ordinary differential equations (ODEs) to estimate pharmacokinetic (PK) parameters related to on-chip liver clearance. …”
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Chemical effects on ecological interactions within a model-experiment loop by Lamonica, Dominique, Charles, Sandrine, Clément, Bernard, Lopes, Christelle

“…We modelled the dynamics of the three species and their interactions using a mechanistic model based on coupled ordinary differential equations. The main processes occurring in this three-species microcosm were thus formalized, including growth and settling of algae, growth of duckweeds, interspecific competition between algae and duckweeds, growth, survival and grazing of daphnids, as well as cadmium effects. …”
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A Multiscale Fractal Approach for Determining Cushioning Curves of Low-Density Polymer Foams by Mariela C. Bravo-Sánchez, Luis M. Palacios-Pineda, José L. Gómez-Color, Oscar Martínez-Romero, Imperio A. Perales-Martínez, Daniel Olvera-Trejo, Jorge A. Estrada-Díaz, Alex Elías-Zúñiga

“…To capture the multiscale nature of the dynamic response behavior of two low-density foams to sustain impact loads, fractional differential equations of motion are used to qualitatively and quantitatively describe the dynamic response behavior, assuming restoring forces for each foam characterized, respectively, by a polynomial of heptic degree and by a trigonometric tangential function. …”
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Integrate mathematical modeling for heat dynamics in two-phase casson fluid flow through renal tubes with variable wall properties by P. Deepalakshmi, Adil Darvesh, Hakim AL Garalleh, Manuel Sánchez-Chero, G. Shankar, E.P. Siva

“…In order to simulate the motion of both fluids and particles, non-linear partial differential equations were employed. The flow through the ureter is exposed to evenly distributed magnetic field in the transverse direction. …”
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The analysis of the influence of the turbulence model selection on the parameters of interaction of a supersonic jet with an obstacle by R. A. Peshkov, A. S. Shmetkova, O. V. Ispravnikova, Ju. L. Suskina

“…The study analyzes the case of interaction of a single supersonic gas jet with a flat barrier oriented perpendicular to the direction of the jet. Differential equations describing the motion of a compressible viscous heatconducting gas (Navier-Stokes equations) are presented, and a method for averaging them by Reynolds is described. …”
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Nonlinear Modelling of Kinetic Data Obtained from Photocatalytic Mineralisation of 2,4-Dichlorophenol on a Titanium Dioxide Membrane by Ignazio Renato Bellobono, Roberto Scotti, Massimiliano D'Arienzo, Franca Morazzoni, Riccardo Bianchi, Rodica Stanescu, Cristina Costache, Liliana Bobirica, Gabriela Cobzaru, Paola Maria Tozzi, Mauro Rossi, Mauro Luigi Bonardi, Flavia Groppi, Luigi Gini

“…For the first series of experiments, a kinetic model was employed, already validated in previous work, from which, by a set of differential equations, four final optimised parameters, k1 and K1, k2 and K2, were calculated. …”
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Influence of Irradiance, Flow Rate, Reactor Geometry, and Photopromoter Concentration in Mineralization Kinetics of Methane in Air and in Aqueous Solutions by Photocatalytic Membra... by Ignazio Renato Bellobono, Mauro Rossi, Andrea Testino, Franca Morazzoni, Riccardo Bianchi, Giulia de Martini, Paola Maria Tozzi, Rodica Stanescu, Cristina Costache, Liliana Bobirica, Mauro Luigi Bonardi, Flavia Groppi

“…A kinetic model was employed, from which, by a set of differential equations, four final optimised parameters, k1 and K1, k2 and K2, were calculated, which is able to fit the whole kinetic profile adequately. …”
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Significance of supervision sampling in control of communicable respiratory disease simulated by a new model during different stages of the disease by Alphonse Houssou Hounye, Xiaogao Pan, Yuqi Zhao, Cong Cao, Jiaoju Wang, Abidi Mimi Venunye, Li Xiong, Xiangping Chai, Muzhou Hou

“…Subsequently, we formulated eight ordinary differential equations that precisely depict the population’s temporal development inside each segment. …”
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Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section by Zhongmin Wang, Rongrong Li

“…Next, dimensionless parameters and variables are introduced for the differential equation and boundary conditions, and the differential quadrature method (DQM) is employed to solve this differential equation with variable coefficients. …”
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Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow by Cui-Cui Sheng, Jin-Zhou Zhao, Yong-Ming Li, Shun-Chu Li, Hu Jia

“…On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. …”
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Terminal-Dependent Statistical Inference for the Integral Form of FBSDE by Qi Zhang

“…Backward Stochastic Differential Equation (BSDE) has been well studied and widely applied. …”
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Fractional derivative in continuous-time Markov processes and applications to epidemics in networks by Matteo D'Alessandro, Piet Van Mieghem

“…Continuous-time Markov processes are governed by the Chapman-Kolmogorov differential equation. We show that replacing the standard time derivative of the governing equation with a Caputo fractional derivative of order 0<α<1, leads to a fractional differential equation whose solution can describe the state probabilities of a class of non-Markovian stochastic processes. …”
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Double-Scale Expansions for a Logarithmic Type Solution to a q-Analog of a Singular Initial Value Problem by Stéphane Malek

“…We examine a linear q−difference differential equation, which is singular in complex time t at the origin. …”
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The Chini integrability condition in second order Lovelock gravity by Mohammed O. E. Ismail, Sunil D. Maharaj, Byron P. Brassel

“…We then determine a systematic approach to integrate the condition of pressure isotropy by showing that the canonical form is a Chini differential equation. The Chini invariant, which allows the master differential equation to be separable, is identified. …”
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Asian Option Pricing with Transaction Costs and Dividends under the Fractional Brownian Motion Model by Yan Zhang, Di Pan, Sheng-Wu Zhou, Miao Han

“…The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. …”
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On the Possibility of the Jerk Derivative in Electrical Circuits by J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, V. H. Olivares-Peregrino

“…For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02.…”
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Similarity Solution for Fractional Diffusion Equation by Jun-Sheng Duan, Ai-Ping Guo, Wen-Zai Yun

“…Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. …”
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A Generalized Solow-Swan Model by Donghan Cai, Hui Ye, Longfei Gu

“…By introducing generalized exogenous variables into the classical Solow-Swan model, we obtain a nonautomatic differential equation. It is proved that the solution of the differential equation is asymptotically stable if the generalized exogenous variables converge and does not converge when one of the generalized exogenous variables persistently oscillates.…”
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Recognition of High Difference Features in Urban Planning Images Based on Morphological Filtering by Peipei Liu

“…This paper mainly studies the image enhancement method based on partial differential equation. By analysing the combination of partial differential equation theory and enhancement, aiming at the shortcomings of low recognition accuracy, high error rate, and long time consuming in the current method of urban planning image feature recognition, a feature enhancement and simulation of urban planning image based on partial differential equation method is proposed; the preprocessing of urban planning image is realized by collecting the urban planning image. …”
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NONLINEAR DYNAMICS ANALYSIS OF DIAPHRAGM COUPLING SYSTEMS WITH ANGULAR MISALIGNMENT by SHENTU LiuFang, ZHAO QingJia, YANG Ping, QIN ShaoBo, SUN YaJun

“…Later,the differential equation is solved by the numerical method. …”
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